10/6/2019 | Introduction to Gaussian integers, as well as prime and irreducible Gaussian integers
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10/13/2019 | Characterization of which positive integers are sums of squares
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10/20/2019 | We will study the symmetries of frieze patterns, especially those of unimodular frieze patterns. We work toward an interesting result proved by Conway and Coxeter about polygonal structures in frieze patterns. [Show less] |

10/27/2019 | We continue our study of the symmetries of unimodular frieze patterns with some challenge problems. We introduce the result proved by Conway and Coxeter connecting polygonal triangulations to frieze patterns. [Show less] |

11/3/2019 | Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofs [Show less] |

11/10/2019 | Introduction to formal proof writing. Sets, functions, basic combinatorics and number theory proofs [Show less] |

11/17/2019 | [Show less] |

11/24/2019 | [Show less] |

12/8/2019 | A 2 hour long math competition against the other high school group! [Show less] |

1/12/2020 | We introduce a new notion of distance - the taxicab metric. We investigate how geometry behaves with this new distance, and try to find similarities and differences between this and the Euclidean metric. [Show less] |

1/19/2020 | We continue our study of metrics, this time considering more abstract examples. We discuss sequences, and we learn that with regards to sequences, the taxicab metric and the Euclidean metric are equivalent. [Show less] |

1/26/2020 | We can extend the integers by including square roots of integers like -1 or 3. Can we predict which prime integers remain prime in the extension? [Show less] |

2/2/2020 | With the help of famous results about quadratic reciprocity we will classify primes in most quadratic extensions of the integers. [Show less] |

2/9/2020 | We will introduce the generating function, a creative, combinatorial tool that can simply solve many interesting problems. By the end, we will have used generating functions to study the Fibonacci sequence, dice games, and ways to pay the unlucky cashier with coins. [Show less] |

2/23/2020 | [Show less] |

3/1/2020 | [Show less] |

3/8/2020 | [Show less] |

3/15/2020 | [Show less] |

4/5/2020 | Travel back in time and revisit some of the old topics from Winter 2020 [Show less] |

4/12/2020 | We revisit metrics, this time with the goal of understanding fixed points. [Show less] |

4/19/2020 | We discuss some interesting graph theory, as well as a strange application to fixed points [Show less] |

4/26/2020 | [Show less] |

5/3/2020 | [Show less] |

5/10/2020 | [Show less] |

5/17/2020 | [Show less] |

5/31/2020 | [Show less] |

6/7/2020 | [Show less] |